metre per second

Assume you have a curve γ:[a,b]→Rd and φ:[a,b]→[a,b] is a reparametrization, i.e., φ′(t)>0. Then you can prescribe any speed function for your parametrization. Given a function σ:[a,b]→R>0, define φ via the ODE φ′(t)=σ(t)|γ′(φ(t))|.

Parametrization, also spelled parameterization, parametrisation or parameterisation, is the process of defining or choosing parameters.

Most parameterization techniques focus on how to “flatten out” the surface into the plane while maintaining some properties as best as possible (such as area). These techniques are used to produce the mapping between the manifold and the surface.

transitive verb. : to express in terms of parameters.

In computer programming, a parameter or “argument” is a value that is passed into a function. Most modern programming languages allow functions to have multiple parameters.

A parameterized function is a function that acts on some arguments, but the way it acts is based on an external constant. A class of functions is the set of all functions that a parameterized function can take. In this example, we see that class1 is a set that contains a function for each integer value.

So, x−a is parallel to v if and only if x−a=tv for some t∈R. We usually write this condition for x being on the line as x=tv+a. This equation is called the parametrization of the line, where t is a free parameter that is allowed to be any real number.

A parametrization of a curve is a map r(t) = from a parameter interval R = [a, b] to the plane. The functions x(t), y(t) are called coordinate functions. The image of the parametrization is called a parametrized curve in the plane. As t varies, the end point of this vector moves along the curve.